All ECAT tests in Pakistan for pre-engineering and ICS students have a math section. ECAT math tests are MCQ based exams that derive from the intermediate curriculum. Details of ECAT math topics are given in the next section.

Additionally, some exams like the FAST university entry test or the NTS NAT for COMSATS also have a basic math or quantitative reasoning section, which test students’ basic math, problem solving and critical thinking skills. In some tests, the math section is the largest and has the most weightage. For instance, in the NUST entry Test (NET), the math section is worth 40% and consists of 80 questions. For more details on which universities accept ECAT, click here. And for various test patterns, visit this link.

This article will go into detail about ECAT math MCQs, ECAT math syllabus, ECAT math shortcuts, ECAT math tricks, ECAT math notes, and also give you some ECAT math MCQs with answers.

Math ECAT MCQs are usually derived from the intermediate or adjacent curriculums. They test students’ knowledge and skills in topics of algebra, trigonometry, calculus and analytic geometry. While all these topics should be familiar to student having studied mathematics in intermediate or A levels, the format of these tests and the question type can be new to them. This is why learning ECAT math tricks and shortcuts is very important.

For in depth understanding of all ECAT math MCQ topics, you can go through math topical video lectures on Maqsad App. These lectures go over each concept in detail, and also solve practice questions using ECAT math shortcuts, and tips and tricks.

- Number Systems
- To learn more about this topic, click here!
- To attempt free tests for this topic, visit the following links:

- Matrices and Determinants
- Quadratic Equations
- Partial Fractions
- Sequences and Series
- Permutation and Combination
- Probability
- Mathematical Induction and Binomial Theorem
- Fundamentals of Trigonometry
- Trigonometric Identities
- Solutions of Triangles
- Trigonometric Graphs and Inverses
- Trigonometric Equations
- Functions and Limits
- Differentiation
- Integration
- Analytic Geometry and Straight Lines
- Circles, Ellipses, Parabolas and Hyperbolas
- Linear Inequalities and Linear Programming
- Vectors
- Exponents and Logarithms

In addition to these, some tests have a basic math or quantitative reasoning section. These sections contain word problems to test students’ comprehension, critical thinking and problem solving skills and are generally from topics of arithmetic, algebra, and geometry. You can watch video lectures for these topics here, and practice topical tests here.

Topics that are tested could include (but are not limited to):

- Averages and Weighted Averages
- To learn more about this topic, click here!
- To attempt free tests of this topics, visit the following links:

- Fractions
- Ratio and Proportion
- Work
- Speed, Time, and Distance
- Percentages
- Selling Price, Cost, and Profit
- Simple and Compound Interest

To go through ECAT math topical tests for each of these topics, click here!

This section contains an ECAT math test, with MCQs from ECAT math past papers. This will serve not only as a good source for sample questions but also as an ECAT math mock test to check your preparation level. To help you gauge your skill level in various topics, topic and difficulty level for each question is also given.

Below is a list of sample ECAT math MCQs with answers.

- The product of two complex conjugate numbers is
- A real number
- An imaginary number
- Always zero
- Not defined

Topic:**Number Systems**

Difficulty Level:**Medium**

- If E = {months of the year}, F = {months with exactly 30 days }, G = {months with exactly 31 days}, then which one of the following is correct?
- G ⊆ F
- F ⊆ G
- G ⊂ E
- E ⊆ F

Topic:**Sets and Functions**

Difficulty Level:**Easy**

- If any two columns of a square matrix A are interchanged then |A| =?
- 0
- 1
- Multiplicative inverse of the determinant of the original matrix
- Additive inverse of the determinant of the original matrix

Topics:**Matrices and Determinants**

Difficulty Level:**Easy**

- If discriminant is positive and perfect square, then roots are
- Real and equal
- Imaginary and distinct
- Real, rational and distinct
- Real, irrational and distinct

Topic:**Quadratic Equations**

Difficulty:**Medium**

- How many partial fractions will there be in the expansion of the above fraction:
- 1
- 2
- 3
- 4

Topic:**Partial Fractions**

Difficulty Level:**Medium**

- What is the sum of series 1+4+16+……….. to 10 terms:

Topic:**Sequences and Series**

Difficulty Level:**Hard**

- In how many ways can 3 English, 2 Urdu and 2 Math books be arranged on a shelf so as to keep all the books in each language together?
- 144
- 288
- 72
- 24

Topic:**Permutation and Combination**

Difficulty Level:**Hard**

- A die is rolled once. Find the probability of getting a number > 4?
- 2/3
- 1
- 1/3
- 1/2

Topic:**Probability**

Difficulty Level:**Medium**

- The coefficient of third term of the binomial expression given above is
- 10
- 20
- 30
- None of these

Topic:**Mathematical Induction and Binomial Theorem**

Difficulty Level:**Medium**

- The above expression is equal to:
- 1 + 2sinAcosA
- 1 - 2sinAcosA
- 2sinAcosA – 1
- 2sinAcosA + 1

Topic:**Trigonometric Identities**

Difficulty Level:**Medium**

- A slide should be built in a park that has to be set up at 10 meters height and also 10 meters away from the support. What should be the angle of elevation?
- 30
- 45
- 60
- 90

Topic:**Fundamentals of Trigonometry**Difficulty Level:

**Medium**

- If triangle of base 6 units has the same areas as a circle of radius 6 units. What is the altitude of the triangle?
- 10π
- 12π
- 6π
- None of these

Topic:**Solutions of Triangle**

Difficulty Level:**Medium**

- For the functions given above, what is the limit of f(x) as x approaches a?
- 1.5
- 2
- 0.5
- 0.67

Topic:**Functions and Limits**Difficulty Level:

**Hard**

- If y=sin(2x+3) then the derivative of y with respecto x is:
- 6cos(2x+3)
- 2sec(2x+3)
- 2cos(2x+3)
- None of these

Topic:**Differentiation**

Difficulty Level:**Medium**

- What is the definite integral of x from x = 0 to x = 1?
- 0
- 1/2
- 2
- 3

Topic:**Integration**

Difficulty Level:**Easy**

- If two lines with slopes m and n are parallel, then
- m=n
- m+n=1
- m-n=-1
- mn=-1

Topic:**Analytic Geometry: Straight Lines**

Difficulty Level:**Medium**

- In 2004, 200 workers received pays on hourly basis from 15 dollar per hour to 25 dollar per hour according to the difficulty of assigned tasks. The largest possible amount paid to the workers for 8 working hours is ___________.
- $215
- $165
- $200
- $170

Topic:**Linear Inequalities and Linear Programming**

Difficulty Level:**Medium**

- All radii of a circle are
- unique
- congruent
- imaginary
- none of the above

Topic:**Circles**

Difficulty Level:**Easy**

- What is the vertex of the parabola given above
- (-3, 4)
- (3, -4)
- (3, 4)
- (-3, -4)

Topic:**Parabola, Ellipse, Hyperbola**

Difficulty Level:**Medium**

- The vector that must be added to the vector i-3j+2k and 3i+6j-7k so that the resultant vector is a unit vector along the y-axis is
- 4i+2j+5k
- -4i-2j+5k
- 3i+4j+5k
- Null vector

Topic:**Vectors**

Difficulty Level:**Hard**

You can find the answer key for these ECAT MCQs with answers at the end of this page.

For similar articles about other subjects, visit the following sites:

For another free ECAT diagnostic test, click here.

For more details on ECAT Past Papers, you can look though this article.

Since most ECAT tests are MCQ based and have a strict and short time limit, students need to learn quick ways to solve these questions. There is no need to show your working as long as you arrive at the correct answers. Some tests also do not allow calculators so students need to brush on their mental math as well.

The first thing that need to do for mental math is memorize your times tables, the squares and square roots and cubes and cube roots of at least the first 20 natural numbers. Usually these arithmetic guides and important formulas are given in ECAT math notes.

You should also memorize the trigonometric ratios for special angles. There’s a few tricks for easily remembering these, some are discussed in our video lectures. This is very useful for solving ECAT MCQs with answers.

You should also memorize all relevant ECAT math formulae. These will also be provided in Maqsad’s ECAT math notes to students to sign up to our batch.

There are also ECAT math shortcuts for solving questions related to matrices, quadratics, sequences, probability, calculus etc. All of these are discussed in our live classes and video lectures.

You can also make use of Test-Taking Strategies such as triaging the test, eliminating the wrong answers and guessing (if there is no negative marking!)

**STRATEGY 1: TRIAGING THE TEST**

You do not need to complete questions in order. To triage the test effectively, do the following:

- First, work through all the easy questions you can do quickly. Skip the questions that are hard or time-consuming
- Second, work through the questions that are doable but time-consuming
- Third, work through the hard questions
- If you run out of time, pick a Letter of the Day for remaining questions

A Letter of the Day is an answer choice letter (A, B, C, or D) that choose to select for questions you guess on.

**STRATEGY 2: ELIMINATION**

If you can determine that one or more answer choices are definitely incorrect, you can increase your chances of getting a right answer by paring the selection down. To eliminate answer choices, do the following:

- Read each answer choice
- Cross out the answer choices that are incorrect
- Remember: there is no negative marking so take your best guess

**STRATEGY 3: GUESSING**

Each MCQ usually has four options and no negative marking (in some tests). That means if you have no idea how to approach a question, you have a 25 percent chance of choosing the correct answer. Even though there’s still a 75 percent chance of selecting an incorrect answer, you won’t lose any points for doing so. The worst that can happen is that you earn zero points on a question, which means you should always at least take a guess, even when you have no idea what to do. When guessing on a question do the following:

- Always try to strategically eliminate answer choices before guessing
- If you run out of time, or have no idea what a question is asking, pick a Letter of the Day.

More ECAT math tricks and ECAT math shortcuts are discussed in Maqsad’s Live Classes and Video Lectures, and will be catered through ECAT math notes provided to our batch.

It is very important to dedicate time to prepare for ECAT tests. While the concepts may seem familiar, the format of questions and paper patterns are new to most students.

To get more details about ECAT tests and resources, click here!

Start by giving a diagnostic test. This will tell you where you stand and which topics you need to focus on.

To revise your concepts and strengthen your understanding, use our detailed Video Lectures.

The main component of your preparation is practice. For lots of topical practice and FLPs, you can use Maqsad’s tests.

To sign-up for Maqsad’s ECAT Batch 2025, click here!

This is the key for ECAT MCQs with answers given in this article.

Hopefully you found these ECAT MCQs with answers helpful in your journey to reach your dream engineering or computing university. For more articles like this, visit Maqsad’s ECAT Blog.

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